_A sad accident turned to a good account.--One example worth a
hundred precepts.--The Centres of Magnitude and Gravity.--The
Point of Suspension.--The Line of Direction.--The stability of
bodies, and upon what it depends.--Method of finding the centre
of gravity of a body.--The art of the Balancer explained and
illustrated.--Various balancing toys._
Just as Mr. Seymour was, on the following morning, stepping upon the
lawn, with the intention of joining his children, Rosa and Fanny both
made their appearance completely drenched with water, and dripping like
mermaids.
“Heyday!” exclaimed their father, “how has this misfortune happened?”
“Do not be angry, papa,” said Tom; “indeed, indeed, it was an accident.
Fanny, observing the water-cart in the garden, had just begun to wheel
it forward, when the water rushed over her like a wave of the sea, and,
upon stopping the cart, it flew over with equal force on the opposite
side, and deluged poor Rosa, who was walking in front of it.”
“Well, well, lose no time in changing your clothes, and meet me again
in half an hour.”
At the appointed time the children reassembled on the lawn.
“And so then,” said their father, “I perceive that my philosophical
lesson of yesterday has been entirely lost upon you.”
The children were unable to comprehend the meaning of this rebuke; but
Mr. Seymour proceeded:--
“I trust, however, that the accident of this morning will serve to
impress it more forcibly upon your memory: one example is better than a
hundred precepts.”
Tom was more puzzled than ever.
“You have met with an accident; I will endeavour to convert it into a
source of instruction, by showing you how the principles of natural
philosophy may be brought to bear upon the most trivial concerns of
life. You learned yesterday, that a body at rest offers a resistance to
any force that would put it in motion, and that, when in motion, it
equally opposes a state of rest; now let us apply this law for the
explanation of the accident that has just befallen you. The butt was
full of water; when you attempted to wheel it forward, the water
resisted the motion thus communicated to the vessel, and from its _vis
inertiæ_, or effort to remain at rest, rose up in a direction contrary
to that in which the vessel moved, and consequently poured over; by
this time, however, the mass of fluid had acquired the motion of the
cart, when you suddenly stopped it, and the water in endeavouring to
continue its state of motion, from the same cause that it had just
before resisted it, rose up on the opposite side, and thus deluged poor
Rosa.”
Louisa was quite delighted with this simple and satisfactory
application of philosophy, and observed, that she should not herself
mind a thorough soaking, if it were afterwards rewarded by a scientific
discovery.
“I will give you, then, another illustration of the same law of
motion,” said Mr. Seymour, “which, instead of explaining an accident,
may, perhaps, have the effect of preventing one. If, while you are
sitting quietly on your horse, the animal starts forward, you will be
in danger of falling off _backward_; but if, while you are galloping
along, it should stop suddenly, you will inevitably be thrown _forward_
over the head of the animal.”
“I clearly perceive,” said Louisa, “that such would be my fate under
the circumstances you state.”
“Now, then, my dear children, since our friend the vicar cannot attend
us at present, suppose we retire to the library, where I have an
interesting experiment to perform, and a new toy ready for your
inspection.”
In compliance with their father’s wishes, the children cheerfully
returned to the library, when Mr. Seymour presented Louisa with a
BANDILOR. Most of our readers are, doubtless, acquainted with this
elegant toy. It consists of two discs of wood, united to each other by
a small axis, upon which a piece of string is affixed. When this string
is wound round the axis, and the bandilor is suffered to run down from
the hand, the end of the string being held by a loop on the fore
finger, its momentum winds up the string again, and thus it will
continue for any length of time to descend from, and ascend to, the
hand. It affords a good example of the operation of _vis inertiæ_, or
what may, with equal propriety, be termed _the momentum of rotatory
motion_. Its action may be compared to that of a wheel, which, running
down a hill, acquires sufficient momentum to carry it up another. There
are several toys which owe their operation to the same principle, of
which we may particularize the windmill, whose fliers are pulled round
by a string affixed to the axis of the sails. In playing with the
bandilor, a certain address is required to prevent the sudden check
which the toy would otherwise receive when it arrived at the end of the
string, and which would necessarily so destroy its momentum as to
prevent its winding itself up again. Mr. Seymour now informed his young
pupils that he had an experiment to exhibit, which would further
illustrate, in a very pleasing manner, the truth of the doctrine of
_vis inertiæ_. He accordingly inverted a wine-glass, and placed a
shilling on its foot; and, having pushed it suddenly along the table,
the coin flew off, towards the operator, or in a direction opposite to
that in which the glass was moving. He then replaced the shilling, and
imparted to the glass a less sudden motion; and, when it had acquired
sufficient velocity, he checked it, and the coin darted forward,
leaving the glass behind it.
Louisa, upon witnessing this experiment, observed that she felt
satisfied of the correctness of her father’s statement, when he told
her that, if the horse suddenly started forward, when she was at rest,
she would be thrown off behind, and that if it should suddenly stop on
the gallop, she would be precipitated over its head. The children now
arranged themselves around the table, in order to consider several
curious toys which Mr. Seymour had collected for the purpose of
explaining the nature of the _Centre of Gravity_.
“But, in the first place,” said Mr. Seymour, “can you tell me, Tom,
what is meant by _The Centre of Gravity_?”
“Its central point,” answered the boy.
“Certainly not; the central point is termed its centre of _magnitude_,
not that of gravity; and it is only when a body is of uniform density,
and regular figure, that these centres of magnitude and gravity
coincide, or fall in the same spot.”
“I now remember,” cried Tom, “that the centre of gravity is that point,
about which all the parts of a body exactly balance each other.”
“Now you are right; it is, in other words, that point in which the
whole weight, or gravitating influence, of a body is, as it were,
condensed or concentrated, and upon which, if the body be freely
suspended, it will rest with security; and consequently, as long as
this centre is supported, the body can never fall; while, in every
other position, it will endeavour to descend to the lowest place at
which it can arrive.”
“Have all bodies, whatever may be their shape, a centre of gravity?”
asked Louisa.
“Undoubtedly.”
“And you say,” continued Louisa, “that every body will fall, if this
point is not supported.”
“Infallibly. And now, Tom,” said Mr. Seymour, “can you tell me what is
meant by the _line of direction_?”
The young philosopher was unable to answer this question, and his
father, therefore, informed him that, if a perpendicular line were
drawn from the centre of gravity of a body to the centre of the earth,
such a line would be termed the _line of direction_; along which every
body, not supported, endeavours to fall; and he was also informed that,
if this said line fell within the base of a body, such a body was sure
to stand; but never otherwise.
Louisa observed that she was not quite sure she understood her papa’s
meaning, and therefore begged for further explanation.
[Illustration: Fig. 10. Overloaded cart with plumb line hanging from
its center of gravity to outside its base of support.]
[Illustration: Fig. 11. Properly loaded cart with plumb line hanging
from its center of gravity to inside its base of support.]
“I will exemplify it then,” replied Mr. Seymour, “by a drawing. Fig. 10
represents a load of stones in a cart moving upon the sloping road
C D E; this load, being low down in the cart, B will represent its
centre of gravity, and B F its line of direction, which, you perceive,
falls much within the supporting or lower wheel G; and there cannot,
therefore, be any danger of such a cart being overturned; but in fig.
11, the centre of gravity is raised from its former position to H, and
H I is now the line of direction; which, falling without the base, or
wheel K, the load will not be supported, and must consequently fall.
These figures,” added Mr. Seymour, “will also explain a fact which you
must have frequently observed, that a body is stable or firm in
proportion to the breadth of its base; hence the difficulty of
sustaining a tall body, like a walking stick, upon its narrow base; of
that of balancing a hoop upon its edge, or a top upon its point; while,
on the contrary, it is almost impossible to upset the cone or the
pyramid, since, in the latter cases, the _line of direction_ falls
within the middle of the base, the centre of gravity of the body being
necessarily low.”
“I suppose,” observed Louisa, “that this is the reason why carriages,
when too much loaded, are so apt to upset.”
“Say, when too much loaded on their _tops_, and you will be right. As
you now, I trust, understand this part of the subject, let us proceed a
step farther: if you take any body, with a view to suspend it, is it
not evident, that if it be suspended by that point in which the centre
of gravity is situated, it must remain at rest in _any_ position
indifferently?”
“I thought,” said Tom, “we had already settled that question.”
“True, my dear boy; but there is another question of great importance
arising out of it, and which you have not yet considered: tell me,
should the body be suspended on any other point, in what position it
can rest?”
“I do not exactly understand the question.”
“There are,” replied his father, “only two positions in which it could
rest, either where the centre of gravity is exactly _above_, or exactly
_below_, the point of suspension; so that, in short, this point shall
be in the _line of direction_. Where the point of suspension is _below_
the centre of gravity, it is extremely difficult to balance or support
a tall body by such a method, because the centre of gravity is always
endeavouring to get under the point of support. Look at this diagram,
and you will readily comprehend my meaning. K is the centre of gravity
of the diamond-shaped figure, which may be supported, or balanced, on a
pin passing through it at M, as long as the centre of gravity K is
immediately over the point of suspension M: but if that centre is
removed in the slightest degree, either to the right or left of its
place K, the body will no longer retain its erect position I K L, but
it will revolve upon M, and place itself in the situation indicated by
the dotted lines beneath the point M: and its centre of gravity will
now be removed to N, directly _under_ M, and in the line K L, which, as
you well know, is the line of direction. Have I rendered myself
intelligible?”
[Illustration: Fig. 12. Diagram of a kite’s center of gravity.]
“I understand it perfectly,” answered Tom.
“And do you also, my dear Louisa?”
Louisa’s answer was equally satisfactory, and Mr. Seymour went on to
state that the information they had now acquired would enable them to
ascertain the situation of the centre of gravity of any plane surface
which was portable, notwithstanding it might possess the utmost
irregularity of shape.
“You shall, for example,” continued he, “find the centre of gravity in
your kite.”
“I cannot say,” observed Tom, “how I should set about it.”
“Well, fetch your kite, and I will explain the method.”
Tom soon produced it, and the tail having been removed, Mr. Seymour
proceeded as follows:--
[Illustration: Fig. 13. Kite viewed right side up.]
“I now,” said he, “suspend the kite by the loop at its bow, and since
it is at rest, we know that the centre of gravity must be exactly below
the point of suspension; if, therefore, we draw a perpendicular line
from that point, which may be easily done by a plumb-line, with a
weight attached to it, such a line will represent the _line of
direction_ (as indicated by A B in fig. 13)”.
“It is clear enough,” said Tom, “that the centre of gravity must lie in
the line A B, but how are we to find in what part of it?”
“By suspending the kite in another direction,” answered Mr. Seymour,
who then hung it up in the position represented at fig. 14, “and then
by drawing another perpendicular from the new point of suspension.”
[Illustration: Fig. 14. Kite viewed at a diagonal.]
“The centre of gravity,” said Louisa, “will in that case be in the line
_c d_, as it was before in that of _a b_.”
“In both the lines!” exclaimed Tom, with some surprise; “it cannot be
in two places.”
“And therefore,” added Mr. Seymour, “it must be in that point in which
the lines meet and cross each other:” so saying, he marked the spot _g_
with his pencil, and then told his little scholars, that he would soon
convince them of the accuracy of the principle. He accordingly placed
the head of his stick upon the pencil mark, and the kite was found to
balance itself with great exactness.
“True, papa,” said Tom, “that point must be the centre of gravity, for
all the parts of the kite exactly balance each other about it.”
“It is really,” observed Louisa, “a very simple method of finding the
centre of gravity.”
“It is,” said Mr. Seymour; “but you must remember that it will only
apply to a certain description of bodies: when they are not portable,
and will not admit of this kind of examination, their centres of
gravity can only be ascertained by experiment or calculation, in which
the weight, density, and situation of the respective materials must be
taken into the account. Having proceeded thus far, you have next to
learn that the centre of gravity is sometimes so situated as not to be
_within_ the body, but actually at some distance from it.”
“Why, papa!” exclaimed Tom, “how can that possibly happen?”
“You shall hear. The centre of gravity, as you have just said, is that
point about which all the parts of a body balance each other: but it
may so happen that there is a vacant space at this point. Where, for
example, is the centre of gravity of this ring? Must it not be in the
space which the ring encircles?”
“I think it must,” said Tom; “and yet how can it be ever supported
without touching the ring?”
[Illustration: One ring supported by a string, and another ring
balanced on a finger.]
“That point cannot be supported,” answered his father, “unless the ring
be so held that the line of direction shall fall within the base of the
support, which will be the case whether you poise the ring on the tip
of your finger, or suspend it by a string, as represented in the
figures which I have copied from the ‘Conversations on Natural
Philosophy.’ I need scarcely add, that it will be more stably supported
in the latter position, because the centre of gravity is below the
point of suspension; whereas in the former the base is extremely
narrow, and it will, consequently, require all the address of the
balancer to prevent the centre of gravity from falling beyond it. As
you are now in possession of all the leading principles upon which the
operations of the centre of gravity depend, I shall put a few practical
questions to you, in order that I may be satisfied you understand them.
Tell me, therefore, why a person who is fearful of falling, as, for
instance, when he leans forward, should invariably put forward one of
his feet, as you did the other day, when you looked into Overton well?”
“To increase his base,” answered Tom; “whenever I lean greatly forward,
I should throw the line of direction beyond it, did I not at the same
instant put out one of my feet, so as to extend my base, and thus to
cause the line to continue within it.”
“Rightly answered; and, for the same reason, a porter with a load on
his back leans forward, to prevent his burthen from throwing the line
of direction out of the base behind. So the horse, in drawing a heavy
weight, instinctively leans forward, in order to throw the whole of his
weight as a counterbalance; and yet,” observed Mr. Seymour, “we are in
the habit of ignorantly restraining him by a bearing rein, in
consequence of which he has to call in the aid of his muscles, by which
a very unnecessary exhaustion of strength is produced. Thus is it that
German and French horses draw heavy weights with apparently greater
ease to themselves, because the Germans tie a horse’s nose _downwards_,
while the French, more wisely, leave them at perfect liberty. But to
proceed. Did you ever observe the manner in which a woman carries a
pail of water?”
“To be sure,” said Tom; “she always stretches out one of her arms.”
“The weight of the pail,” continued Mr. Seymour, “throws the centre of
gravity on one side, and the woman, therefore, stretches out the
opposite arm, in order to bring it back again into its original
situation; did she not do this, she must, like the English draught
horses, exert her muscles as a counteracting force, which would greatly
increase the fatigue of the operation: but a pail hanging on each arm
is carried without difficulty, because they balance each other, and the
centre of gravity remains supported by the feet.”
“I see,” said Louisa, “that all you have said about the woman and her
pail must be true; but how could she have learned the principle which
thus enabled her to keep the centre of gravity in its proper place?”
“By experience. It is very unlikely that she should ever have heard of
such a principle, any more than those people who pack carts and
waggons, and yet make up their loads with such accuracy as always to
keep the line of direction in, or near, the middle of the base. But to
proceed to another example--have I not frequently cautioned you against
jumping up suddenly in a boat? Can you tell me upon what principle such
an operation must be attended with danger?”
“I suppose,” said Tom, “for the very same reason that a waggon is more
likely to be overturned when its top is too heavily laden; it would
elevate the centre of gravity, and thereby render the line of direction
liable to be thrown beyond the base, and so upset the boat.”
Mr. Seymour observed, that after this lesson he thought the balancing
which Tom and Louisa had witnessed at Astley’s theatre, last year,
would cease to appear so miraculous. Louisa declared that she had now
discovered the whole mystery.
“You have doubtless perceived,” said her father, “that the art entirely
consists in dexterously altering the centre of gravity upon every new
position of the body, so as constantly to preserve the line of
direction within the base. Rope-dancers effect this by means of a long
pole, the ends of which are loaded by weights, and which they hold
across the rope. If you had paid sufficient attention to their
movements, you must have perceived how steadily they fixed their eyes
on some object near the rope, so as to discover the slightest deviation
of their centre of gravity to one or the other of its sides, which they
no sooner detect, than they instantly rectify it by a countervailing
motion of their pole, and are thus enabled to preserve the line of
direction within the narrow base. This very same expedient is
frequently practised by ourselves; if we slip or stumble with one foot,
we naturally extend the opposite arm, making the same use of it as the
rope-dancer does of his pole. Many birds, also, by means of their
flexible necks, vary the position of their centre of gravity in the
same manner. When they sleep, they turn it towards the back, and place
it under the wing, in order to lay the greatest weight on the point
above the feet.”
“What an interesting subject this is,” cried Louisa, “and how many
curious things it is capable of explaining!”
“Indeed is it; and I shall take an opportunity of pointing out several
specimens of art (9) which are indebted for their stability to the
scientific application of the principle we have been considering;--but
I have now a paradox for you, Tom.”
“Let us hear it, papa.”
“How comes it that a stick, loaded with a weight at the upper
extremity, can be kept in equilibrio, on the point of the finger, with
much greater ease than when the weight is near the lower extremity, or,
for instance, that a sword can be balanced on the finger much better
when the hilt is uppermost?”
“That is indeed strange. I should have thought,” replied Louisa, “that
the higher the weight was placed above the point of support, the more
readily would the line of direction have been thrown beyond the base.”
“In that respect you are perfectly right; but the balancer will be able
to restore it more easily in one case than in the other; since, for
reasons which you will presently discover, the greater the circle which
a body describes in falling, the less will be its tendency to fall.
Look at the sketch which I have prepared for the explanation of this
fact, and I think you will readily comprehend the reason of it.
[Illustration: Man balancing a sword in each hand, hilt up in one, hilt
down in other, showing arc of centres of gravity for each.]
“When the weight is at a considerable distance from the point of
support, its centre of gravity, in deviating either on one side or the
other from a perpendicular direction, describes a larger circle, as at
_a_, than when the weight is very near to the centre of rotation or the
point of support, as at _b_. But, in a large circle, an arc of any
determinate extent, such as an inch, for example, describes a curve
which deviates much less from the perpendicular than if the circle were
less; as may be seen by comparing the positions of the sword at _d_ and
_e_; and the sword at _d_ will not have so great a tendency to deviate
farther from the perpendicular, as that at _e_; for its tendency to
deviate altogether from the perpendicular is greater, according as the
tangent to that point of the arc, where it happens to be, approaches
more to the vertical position. You see then that it is less difficult
to balance a tall, than a shorter pole; and it is for the same reason
that a person can walk with greater security on high than on low
stilts.”
“That is very clear,” said Louisa, “although, before your explanation,
I always associated the idea of difficulty with their height.”
“I suppose,” added Tom, “that the whole art of walking on stilts may be
explained by the principles you have taught us.”
“Undoubtedly it may; for the equilibrium is preserved by varying the
position of the body, and thus keeping the centre of gravity within the
base.”
“It must be a great exertion,” observed Louisa.
“Before custom has rendered it familiar; after which, there is no more
fatigue in walking on stilts, than in walking on our feet. There is a
district in the south of France, near Bourdeaux, called the Desert of
Landes, which runs along the sea coast between the mouths of the Adour
and Gironde, where all the shepherds are mounted on stilts; on which
they move with perfect freedom, and astonishing rapidity; and so easily
does habit enable them to preserve their balance, that they run, jump,
stoop, and even dance, with ease and security.”
“How very odd!” said Tom; “what can be their motive for such a strange
habit?”
“Its objects,” replied his father, “are important: to keep the feet out
of the water, which, during the winter, is deep on the sands; and to
defend them from the heated sand during the summer; in addition to
which, the sphere of vision over so perfect a flat is materially
increased by the elevation, and the shepherds are thus enabled to see
their flocks at a much greater distance.[9] They cannot, however, stand
perfectly still upon their stilts, without the aid of a long staff,
which they always carry in their hands; this guards them against any
accidental trip, and, when they wish to be at rest, forms a third leg
that keeps them steady.”
“I suppose,” said Louisa; “that the habit of using these stilts is
acquired while they are very young.”
“It is, my dear: and it appears that, the smaller the boy is, the
higher are his stilts; a fact which affords a practical proof of the
truth of what I have just stated.”
“The stork is said, in my work on Natural History, to be always walking
on stilts,” said Louisa; “and yet it does not appear to fatigue him.”
“That is very true,” replied the father; “but you must remember, that
nature has furnished the bird with a provision, by which the legs are
kept extended without any exertion of the muscles, in the manner of
certain springs; a structure which enables it to pass whole days and
nights on one foot, without the slightest fatigue. If you will visit
the cook the next time she trusses a fowl, you will at once perceive
the nature and utility of this structure; upon bending the legs and
thighs up towards the body, you will observe that the claws close of
their own accord; now, this is the position of the limbs in which the
bird rests upon its perch, and in this position it sleeps in safety,
for the claws do their office in keeping hold of the support, not by
any voluntary exertion, but by the weight of the body drawing the
strings tight.”
“But, papa,” said Tom, “I have yet some more questions to ask you on
the subject of balancing. I am not at all satisfied about many of the
tricks that we saw last year; indeed, I cannot believe, that many of
those astonishing feats can be explained by the rules you have just
given us.”
“I very well know to what you allude,” replied Mr. Seymour. “Many
singular deceptions are certainly practised by removing the centre of
gravity from its natural into an artificial situation, or by disguising
its place; thus, a cylinder placed upon an inclined surface may be made
to run _up_, instead of _down_ hill. I can even appear to balance a
pailful of water on the slender stem of a tobacco-pipe: but I shall be
enabled to explain the nature of these deceptions by some toys which I
have provided for your amusement, and which I must say you are fully
entitled to possess, as a reward for the clear and satisfactory manner
in which you have this day answered my questions. But see! here comes
Mr. Twaddleton: he would really seem to possess an instinct that always
brings him to the Lodge whenever I am preparing some amusement for you.”
The vicar smiled as he entered the room, but, unwilling to interrupt
the lesson, he placed his fore finger on his lip, and, with a
significant nod, silently took a seat at the table. The children
laughed aloud at this cautious demeanour; and Tom exclaimed, “Why, Mr.
Twaddleton, our lesson is over, and we are going to receive some new
toys as a reward.”
“I have here,” said Mr. Seymour, as he opened a large wooden box, “a
collection of figures, which will always raise themselves upright, and
preserve the erect position; or regain it, whenever it may have been
disturbed.”
He then arranged these figures in battalion on the table, and striking
them flat by drawing a rod over them, they immediately started up
again, as soon as it was removed. “These figures,” continued he, “were
bought at Paris some years ago, under the title of _Prussians_.”
“I declare,” exclaimed the vicar, “they remind me of the rebellious
spirits whom Milton represents as saying that ascent is their natural,
and descent their unnatural, motion.”[10]
“I have seen skreens similarly constructed,” said Mrs. Seymour, “which
always rose up, of themselves, upon the removal of the force that had
pressed them down.”
“I will explain their principle,” said Mr. Seymour.
“Suppose we first examine the construction of the figure,” observed the
vicar. “Bless me! why it is like Philotus the poet, who was so thin and
light, that lead was fastened to his shoes to prevent his being blown
away.”
[Illustration: Toy soldier mounted on the flat part of a hemisphere.]
“The figure,” said Mr. Seymour, “is made of the pith of the elder-tree,
which is extremely light, and is affixed to the half of a leaden
bullet; on account, therefore, of the disproportion between the weight
of the figure and that of its base, we may exclude the consideration of
the former, and confine our attention to the latter. The centre of
gravity of the hemispherical base is, of course, in its axis; and
therefore tends to approach the horizontal plane as much as possible,
and this can never be accomplished, until the axis becomes
perpendicular to the horizon. Whenever the curved surface is in any
other position, the centre of gravity is not in the lowest place to
which it can descend, as may be seen by the diagram which I have just
sketched. If the axis _a b_ be removed to _c d_, it is evident that the
centre of gravity will be raised, and that, if left alone, it would
immediately descend again into its original position.”
[Illustration: Fig. 14. Hemisphere shown in two positions using solid
and dotted lines.]
“I understand it perfectly,” said Tom. “When the axis _a b_ is
perpendicular, the centre of gravity will be in its lowest point, or as
near the earth as it can place itself; when, therefore, the figure is
pressed down, the centre of gravity is raised, and, consequently, on
the removal of that pressure, it will descend to its original position,
and thus raise the figure.”
[Illustration: Toy man with sword, turban, and shield, mounted on a
candlestick with weights jutting out and down from both sides.]
“I see you understand it. Here, then,” continued Mr. Seymour, “is
another toy in further illustration of our subject. It consists of a
small figure, supported on a stand by a ball, which is quite loose; and
yet it is made to turn and balance itself in all directions, always
recovering its erect position, when the force applied to it is removed.
The two weights, in this case, bring the centre of gravity considerably
_below_ the point of suspension or support, and therefore maintain the
figure upright, and make it resume its perpendicular position, after it
has been inclined to either side; for the centre of gravity cannot
place itself as low as possible, without making the figure stand erect.”
“That is very evident,” cried Louisa.
“I shall next exhibit to you,” continued Mr. Seymour, “a toy that
furnishes a very good solution of a popular paradox in mechanics; viz.
_A body having a tendency to fall by its own weight, how to prevent it
from falling, by adding to it a weight on the same side on which it
tends to fall._”
“That is indeed a paradox!” exclaimed Louisa. “The next time I see the
gardener sinking under the load of a heavy sack, I shall desire him to
lighten his burden by doubling its weight.”
[Illustration: Toy horse with its back legs on a ledge, with a weight
attached to its belly with a wire which curves back and down under the
ledge.]
“Will you, indeed, Miss Pert? I do not think so, after you have seen
the operation of the toy I am now about to exhibit. Here, you perceive,
is a horse, the centre of gravity of which would be somewhere about the
middle of its body; it is, therefore, very evident that, if I were to
place its hinder legs on the edge of the table, the line of _direction_
would fall considerably beyond the base, and the horse must be
precipitated to the ground; you will, however, perceive that there is a
stiff wire attached to a weight which is connected with the body of the
horse, and by means of such an addition, the horse prances with perfect
security at the edge of the precipice: so that the figure which was
incapable of supporting itself is actually prevented from falling, by
adding a weight to its unsupported end!”
The children admitted the truth of this statement, and were not
immediately prepared to explain it.
“The weight, indeed, appears to be added on that side; but, in reality,
it is on the opposite side,” said the vicar.
“In order to produce the desired effect,” observed Mr. Seymour, “the
wire must be bent, so as to throw the weight far back, under the table;
by which contrivance, since the centre of gravity of the whole compound
figure is thrown into the leaden weight, the hind legs of the horse
thus become the point of suspension, on which the ball may be made to
vibrate with perfect security.”
“Now I understand it,” cried Tom; “instead of the weight supporting the
horse, the horse supports the weight.”
“Exactly so. You perceive, therefore, from these few examples, that the
balancer, by availing himself of such deceptions, and combining with
them a considerable degree of manual dexterity, may perform feats,
which, at first sight, will appear in direct opposition to the laws of
gravity. There is also another expedient of which the balancer avails
himself, to increase the wonder of his performances, and that is the
influence of rotatory motion, which, you will presently see, may be
made to counteract the force of gravity.”
“I remember that the most surprising of all the tricks I witnessed was
one, in which a sword was suspended on a key, which turned round on the
end of a tobacco-pipe; on the top of the sword a pewter-plate was, at
the same time, made to revolve with great velocity.”
“I well remember the trick to which you allude. The rotatory motion
prevented the sword from falling, just as you will hereafter find the
spinning of the top will preserve it in an erect position. There is
also another effect produced by rotatory motion, with which it is
essential that you should become acquainted. You, no doubt, remember
that momentum, or the velocity of a body, will compensate for its want
of matter. A number of bodies, therefore, although incapable of
balancing each other when in a state of rest, may be made to do so, by
imparting to them different degrees of motion. I believe that you are
now acquainted with all the principles upon which the art of balancing
depends; and I have little doubt, should we again witness a performance
of this kind, that you will be able to explain the tricks which
formerly appeared to you so miraculous.”
[Illustration: Three boys using stilts.]
-----
Footnote 9:
In Scotland stilts are used to pass rivers.
Footnote 10:
A The vicar here alludes to the speech of Moloch (Paradise Lost, b.
ii. 1. 75):--
“That in our proper motion we ascend
Up to our native seat: descent and fall
To us is adverse.”
------------------------------------------------------------------------
[Illustration: A man holding a balloon with a face on it, blown up, and
six people laughing at the sight.]